I don't mind following maths as that is what my degree is in but the physics side of it escapes me.
Every circuit element has a mathematical model that describes its physical behaviour.
Here is a resistor:
R
v
1(t) ----/\/\/\/----- v
2(t)
i(t)
The model variables are R (the resistance), v
1 and v
2 (the voltages at each terminal of the resistor), and i (the current through the resistor).
The resistor model says:
v
1(t) - v
2(t) = i(t) R
This (ideal) model is true for every (assumed ideal) resistor in the circuit.
A capacitor:
C
v
1(t) -----| |------ v
2(t)
i(t)
The (ideal) capacitor model says:
i(t) = C d/dt ( v
1(t) - v
2(t) )
This is a linear first order differential equation.
Any circuit consisting of resistors and capacitors can be modelled using these equations.
To complete the model two other equations are needed.
At any junction, the voltages on each branch are equal:
v
1(t) = v
2(t) = v
3(t) = ...
At any junction, the sum of all currents entering and leaving is zero (with appropriate sign convention):
sum( i
1(t), i
2(t), i
3(t), ... ) = 0
With these equations, any circuit consisting of resistors and capacitors can be represented as a system of differential and algebraic equations that can be solved simultaneously with the addition of suitable boundary conditions. One voltage must be assigned a value of zero as a reference voltage (often the negative supply rail in the circuit, but it doesn't have to be). Any input voltages must be provided with a forcing function (the input signal the circuit will respond to).
Transistors can also be given a model. It will be slightly more complicated, but a similar principle applies.
The answer then to the question, "how does the signal know where to go?" is answered by the solution to this system of equations.
In reality, circuit designers have come up with various simpler ways to estimate what circuits will do when given AC signals, but ultimately it all comes down to a system of equations involving voltage, current and time.